Estimation, prediction, and forecasting of urban solar brightness: A comprehensive benchmarking of empirical, hybrid AI, and Deep-NARMAX models

Abstract

Understanding the variability of solar brightness is essential for optimising solar energy systems, improving urban air quality assessments, and enhancing environmental forecasting. The aim of this study is to investigate the influence of meteorological and atmospheric pollutant variables—including temperature, relative humidity, precipitation, wind direction, wind speed, PM₂.₅, PM₁₀, ozone (O₃), carbon monoxide (CO), SO₂, O₃, NO, NO₂, NO_x and others—on incoming solar radiation, using solar brightness as a proxy. A comprehensive dataset spanning five years of hourly observations was analysed. Open-source data from four air quality monitoring stations in Craiova, was provided by the Romanian Environmental Agency. The study followed a five-stage approach. First, data preprocessing was conducted to identify and address anomalies, outliers, and missing values, while trends for solar brightness and other studied variables were analysed. In the second stage, the best global solar radiation (GSR) model among 10 GSR models is selected. In the third stage, correlations between solar brightness and other variables, including data provided by the best GSR model, based on exploratory data analysis, were examined. A deep AI-based hybrid approach was applied in the fourth stage to discover the optimal AI predictive model for solar brightness based on related variables. Finally, a deep NARMAX model was elaborated and applied to model and anticipate next hourly solar brightness in Craiova. A set of statistical metrics was employed to assess the results of the models.